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Ramanujan summation of divergent series

Abstract : In Chapter VI of his second Notebook Ramanujan introduce the Euler-MacLaurin formula to define the " constant " of a series. When the series is divergent he uses this " constant " like a sum of the series. We give a rigorous definition of Ramanujan summation and some properties and applications of it. These properties of the summation seems very unusual so in the last chapter we give a general algebraic view on summation of series that unify Ramanujan summation with the classical summations procedures.
Keywords : Ramanujan summation
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Preprints, Working Papers, ...
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https://hal.univ-cotedazur.fr/hal-01150208
Contributor : Bernard Candelpergher <>
Submitted on : Saturday, May 9, 2015 - 11:03:20 AM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 8:10:23 PM

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  • HAL Id : hal-01150208, version 1

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B Candelpergher. Ramanujan summation of divergent series. 2015. ⟨hal-01150208v1⟩

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